What is the equation of the line normal

Kennedy Ford

Kennedy Ford

Answered question

2022-04-07

What is the equation of the line normal to f(x)=xex at x=7?

Answer & Explanation

fonne0kgq

fonne0kgq

Beginner2022-04-08Added 11 answers

f(7)=7e7
The normal line has to pass through the point (7, f(7))
f(x)=(x+1)ex
f(7)=8e7
Since the normal line is perpendicular to the tangent line, we have the gradient of the normal line, m, given by
m=1f(7)=18e7
The y-intercept of the line is given by
c=y-mx
=7e7(18e7)(7)
=7e7(e14+18)
Equation of normal line in slope-intercept form
y=18e7x+7e7(e14+18)

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